Test 3 Cheat Sheet 2 - CAPM : The CAPM (capital asset...

R 2 = b i 2 s M 2 b i 2 s M 2 + s 2 ( e i ) CAPM : The CAPM (capital asset pricing model) is a theoretical model of equilibrium ex ante or expected returns on risky assets; it is a value-weighted portfolio. Each security is held in a proportion equal to its market value divided by the total market value of all securities. (Assumes that investors are single-period planners who agree on a common input list form security analysis and seek mean-variance optimal portfolios). •Recall the simplifying assumptions that lead to the basic version of the CAPM (necessary for all investors to agree on risky portfolio) 1.Investors are “price takers” and act as if security prices are unaffected by their own trades  no one can manipulate; price it is market determined; necessary to agree on optimal risky portfolio 2. All investors have the same identical single-period planning horizon  heroic assumption 3. Investments are limited to publicly traded financial assets, and to risk-free borrowing and lending (most of the time borrow at a higher rate than risk free) 4. Investors pay no taxes and no transactions costs 5. All investors are rational mean-variance optimizers (very far off assumption) 6. Symmetric information and identical expectations (means we all have the same info set, erroneous for one, then erroneous for all; everyone expects same returns). *Summary of the equilibrium that will prevail in this hypothetical world of securities and investors * 1. All investors will choose to hold a portfolio of risky assets in proportions that duplicate representation of the assets in the market portfolio ( M ), which includes all traded assets. 2.The market portfolio will be the tangency portfolio to the optimal capital allocation line. (This CAL is referred to as the capital market line, or CML.) All investors therefore hold M as their optimal risky portfolio. 3. The risk premium on the market portfolio will be proportional to its risk, and the degree of risk aversion of the representative investor: E ( r M ) -r f = (1) A s M 2 (times risk of market portfolio) Here A is the average level of risk aversion across investors. & σ M 2 is the variance of the market portfolio 4. The risk premium on individual assets will be proportional to the risk premium on the market portfolio ( M ), and the β coefficient of the security, where: 2 ) , cov( M M i i r r β = and E ( r i ) -r f = b i [ E ( r M ) -r f ] = 1 variance /variance All Investors Hold the Market Portfolio : The contribution of the CAPM is to derive the fair price (in terms of the expected return) at which investors are willing to hold each asset in the optimal risky portfolio Expected Returns on Individual Securities: The CAPM is built on the insight that the appropriate risk premium on an individual asset will be determined by its contribution to the risk of the investors’ overall portfolios Recall first that the market portfolio has a risk premium of E(rM) - rf , and a risk-reward ratio of:

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